This is all OSM-based. OSM is one big pile of data - we don't do layers.

It is also best to add it directly into OSM, importing data afterwards is tricky.

My talk at Why25 should be a good intro (https://media.ccc.de/v/why2025-198-openstreetmap-for-beginne...), but the OSM-wiki also contains some valuable sources: https://wiki.openstreetmap.org/wiki/Tags , https://wiki.openstreetmap.org/wiki/Map_features

There are also various libraries to show OSM as background map on a website and allow you to draw features on top. Those support various formats (GPX, GeoJSON, ...) Leaflet and MapLibre are the biggest here, with leaflet being the easiest and MapLibre being very flexible and performant

If by layers you mean tiles, you can make a server providing ZXY tile images. Some OSM clients (e.g. BRouter) allow adding custom tile servers for baselayer and overlays.

https://wiki.openstreetmap.org/wiki/Tile_servers